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Archimedes between legend and fact
Lucio Russo
Published online: 3 August 2013

Centro P.RI.ST.EM, Universita
`
Commerciale Luigi Bocconi 2013
Abstract
The figure of Archimedes that most are familiar
with is depicted in the works of authors such as Vitruvius
and Plutarch, who lived centuries after his death and
transmit an image of the scientist that is deformed by
legend. This paper re-examines what is actually known
about the life of Archimedes and his personality.
Keywords
Archimedes

History of science

History of technology

Diodorus Siculus

Polybius

Pliny the Elder

Cicero

John Zonaras

John Tzetzes

Titus Livius

Plutarch

Galen

Simplicius
Probably no scientist has ever occupied a larger place in the
collective imagination than Archimedes (Fig.
1
). The fig-
ure of Archimedes that most are familiar with is depicted,
however, in the works of authors such as Vitruvius and
Plutarch, who lived centuries after his death and transmit
an image of the scientist that is deformed by legend, one
that already by their day at least partly shrouded his
memory, and one that they themselves contributed to, at
least in part. It is thus useful to re-examine what we really
know about the life of Archimedes and his personality.
There are few biographical facts that are absolutely
certain. There is no doubt that Archimedes was a Syracu-
san, and that he died during the Roman sack of Syracuse in
212
B
.
C
. His date of birth is much less certain. It is thought
that he was born in 287
B
.
C
.—in fact, this year we celebrate
the twenty-third centenary of his birth—but the only author
who gives this date is the Byzantine John Tzetzes, of the
twelfth century, according to whom Archimedes died at the
age of 75 [
Chiliades
, II, 108]. It is possible that Tzetzes had
reliable sources at his disposal that we do not know about,
but it might also be that he (or his source) wished only to
quantify the fact, mentioned by several authors, that he
died when he was old. We will see that we have good
reasons not to place too much faith in his testimony. The
news that he was the son of the astronomer Phidias, given
in many texts as certain, derives from a passage in
Sand
Reckoner
by Archimedes himself, incomprehensible in the
manuscripts (
Arenario
, II, 136–137, [Mugler 1970–1972
3
]), which the philologist Friedrich Blass in 1883 emended,
conjecturing that it contained the words
Ueidi
9
ad

so
u
̃
a
9
lo
u
̃
pasq
o
`
1
(my father Phidias). Since the context regards
an estimate of the ratio between the dimensions of the sun
and the moon, if the amendment is correct, the hypothetical
father Phidias should presumably have dealt with astron-
omy on at least one occasion, but no other source cites an
astronomer by that name.
I don’t believe there is any reason to doubt Plutarch’s
statement (
Vita Marcelli
, 14, 7) that Archimedes, in addi-
tion to being friends with, was also a relative (
rtccem

g1
)of
the tyrant of Syracuse Hieron I, although to some that
information seems to contradict a passage of Cicero.
1
It is also certain that Archimedes spent time in Alex-
andria. Diodorus Siculus (
Bibliotheca historica
, V, 37, 3)
tells us that Archimedes invented the screwpump when he
was in Egypt. Moreover, the terms used by Archimedes in
L. Russo (
&
)
Dipartimento di Matematica, Universita
`
di Roma ‘‘Tor Vergata’’,
Via della Ricerca Scientifica, 1, 00133 Rome, Italy
e-mail: russo@mat.uniroma2.it
1
Cicero (
Tusculanae disputationes
, V, 23) says that he wants to
contrast the life of Dionysius I of Syracuse with that of a man who is
humble and common (
humilem homunculum
) from the same city:
Archimedes. It does not seem to me that this passage must necessarily
be interpreted as a reference to Archimedes’ humble origins; Cicero
might only have wished to underline the distance between a sovereign
and a private citizen.
123
Lett Mat Int (2013) 1:91–95
DOI 10.1007/s40329-013-0016-y
lamenting the death of Conon of Samos (
De sphaera et
cylindro
,I,9;
De lineis spiralibus
, II, 8), who was active in
Alexandria, lead us to presume that he had known him
personally.
The biographical facts on which the sources dwell the
most regard Archimedes’ contribution to the defence of
Syracuse during the Roman siege of 212
B
.
C
. and his death
during the sack of that city. The best source for the siege,
due both to his nearness to the events and for his general
reliability, is Polybius (
Historiae
, VIII, chaps. 3–7). In his
account, the historian describes war machines conceived by
Archimedes, and in particular the various kind of weapons
for launching projectiles and the
manus ferrea
(
ve

iq
ridgq
~
a
) or claw, manoeuvred from inside the wall, used to
overturn Roman ships as they drew near. Polybius
(
Historiae
, VIII, 7) underlines the importance of Archi-
medes’ contribution to the defence of the city, writing
among all else:
Such a great and marvellous thing does the genius of
one man show itself to be when properly applied to
certain matters. The Romans at least, strong as they
were both by sea and land, had every hope of cap-
turing the town at once if one old man of Syracuse
were removed; but as long as he was present, they did
not venture even to attempt to attack in that fashion in
which the ability of Archimedes could be used in the
defence [Polybius 1922
6
, III, 462–463].
In Polybius, who wrote in the second century
B
.
C
., there
is no trace of the episodes during the siege that most
nourished the legend of Archimedes: the construction of
the burning mirrors and the circumstances of his death
(Fig.
2
).
At the time it must have seemed completely natural that
Archimedes did not survive the attack on the city. The idea
that the commander of the Romans, Marcellus, lamented
the death of the elderly scientist appears only a century
later and for the first time in a writing of Cicero (
In Verrem
,
II, 4, 131), who was also the first to recount how, when the
Romans conquered Syracuse, Archimedes was so absorbed
in the study of geometric figures that he didn’t notice it (
De
finibus
, V, 50). It is well known that Cicero also boasted of
having found Archimedes’ tomb when he was quaestor in
Sicily: he claims to have recognised it by the drawing of a
sphere inscribed in a cylinder etched into it. The Syracu-
sans themselves had told him that that etching indicated the
tomb of Archimedes, which, moreover, was located where
one might have expected, that is, in the city cemetery. And
yet many believed Cicero’s strange boast.
Gradually, as the facts faded into the past, the details of
Archimedes’ death were embellished and the Romans’
responsibility for it was played down. In Pliny the Elder’s
Natural History
appears for the first time the information
that Archimedes was killed in violation of Marcello’s
explicit orders to spare him (
Naturalis Historia
, VII, 125).
Valerius Maximus (
Factorum et dictorum memorabilium
libri IX
, 8.7, ext 7) also tells of Archimedes’ last words,
which asked his assassin not to ruin the geometric figure he
had just drawn. Around 100
A
.
D
. Plutarch not only wrote of
the death of the scientist, giving various alternate versions
of the circumstances (
Vita Marcelli
, 19, 4–5), but also
seems to know other details of Marcellus’s behaviour,
which appears to be even more laudable. The Roman
commander, encountering Archimedes’ killer, is said to
have turned his gaze away in a sign of disdain, and to have
Fig. 2
The death of Archimedes from an illustration from
Beacon
Lights of History
, after a painting by Edouard Vimont (1846–1930)
Fig. 1
Bust of Archimedes by Luciano Campisi (1859–1953). Photo:
Giovanni Dall’Orto
92
Lett Mat Int (2013) 1:91–95
123
wished to honour the scientist’s relatives (
Vita Marcelli
,
19, 6).
In the Byzantine authors John (Ioannes) Zonaras and
John Tzetzes the details become even more precise. They
even knew the last two sentences pronounced by Archi-
medes before he died ([
10
], II, 264, 24–265, 2)—even
though the two versions don’t agree even partially. In the
work by Tzetzes in particular there are new elements. Not
only does he maintain that Archimedes attempted to defend
himself, asking for a weapon, but he also conjectures that
Marcellus had the killer executed (
Chiliades
, II, 134–155).
These details, of course fanciful, cast much doubt on the
reliability of Tzetzes report of Archimedes’ age.
The invention of the details of Archimedes’ death con-
tinued up until recent periods. According to many books
(and innumerable Internet sites), Archimedes words to the
Roman soldier who was about to kill him were
Noli turbare
circulos meos
(this phrase is even repeated in the relatively
recent book by Dijksterhuis [1987] [
1
]). Sometimes it is
quoted in Greek, in the form
‘
Lg
9
lot so
u
`
1jt
9
jkot1
sa
9
qasse
. Nevertheless, it seems clear that the Greek
expression was translated from Latin, and not the other way
around. In any case, no Greek, Latin or Byzantine author
quotes it, either in Greek or in Latin. It remains to be
discovered who is the first to have introduced the habit of
quoting it, and if among other things he intended the
vaguely obscene allusion with which it is often cited.
Likewise, the testimonies of the episode of the burning
mirrors grow and become more detailed with the passing of
time. Polybius, Titus Livius (who provides a more succinct
account of the siege of Syracuse,
Ab urbe condita libri
CXLII
, XXIV, 34) and Plutarch (who describes the siege in
the
Vita Marcelli
cited earlier) say nothing of it. The first
mentions of Roman ships set afire from a distance thanks to
devices invented by Archimedes appears in the second
century
A
.
D
., in one passage from Lucian (
Ippia
, 2) and one
from Galen (
De temperamentis
, III, 2).
2
Neither of the two,
however, speak of mirrors, and the most plausible inter-
pretation is that they intended to refer to the launching of
incendiary substances. The first clear reference to burning
mirrors dates to the sixth century and is due to Anthemius
of Tralles, who cites the episode as unanimously accepted
by historians (
Peqi
9
paqad
o
́
nxm lgvamgla
9
sxm
, II, 47–48)
and then, in the same work, proposes a conjectural recon-
struction of the form and construction of the mirrors (
Peqi
9
paqad
o
́
nxm lgvamgla
9
sxm
, III, 49–50). In the twelfth
century, Zonaras (
Epitome historiarum
, [Dindorf] vol. II,
263, 2–8) and Tzetzes (
Chiliades
, II, 121–131), authors
already mentioned, describe in detail the mirrors of
Archimedes. Their source—particularly in the case of
Tzetzes—seems to be Anthemius, but details that in An-
themius were explicitly part of the conjectural recon-
struction (for example, the hexagonal shape of the central
mirror) are by now presented as facts.
The development of the testimonies that we have
described renders highly unlikely the use of mirrors in
war, but this does not mean we must necessary deduce
that they were only legend. The description of parabolic
mirrors by Diocles, which we have in an Arabic transla-
tion,
3
which contains a demonstration of the focal prop-
erty of the parabola, is proof that in Antiquity these
devices were effectively designed, and there is no reason
why they might not have been constructed. Archimedes,
who was an expert in parabolas and paraboloids (which he
also used in his treatise
On Floating Bodies
), had written a
voluminous treatise on
Catoptrica
(that is, on mirrors) in
which, according to Apuleius (
Apologia
, 16), were also
found descriptions of mirrors that, when placed facing the
sun, were capable of igniting flammable objects. If this
treatise was the unacknowledged source for Diocles, the
legend of the ships set afire with burning mirrors might
have been created from the mingling of the memory of
Archimedes’ design for such mirrors (perhaps conceived
as a useful substitute for wood) with that of his contriv-
ances with which the Syracusans launched incendiary
substances.
In the other episodes that nourished the legend of
Archimedes it is likewise generally possible to find a kernel
of truth deformed by tradition. One of the most famous is
the phrase ‘Give me a lever and a fulcrum on which to
place it, and I shall move the world!’, cited, with a few
variations, by several authors. The first was Plutarch (
Vita
Marcelli
, 14, 7–9), followed in the fourth century by
Pappus (
Collectio
, VIII, 1060, 1–12 [Hultsch 1876
3
]), in
the sixth century by Simplicius (
In Aristotelis Physicorum
libros commentaria
, 1110, 2–5 [1882] [
9
] and Olympiod-
orus (
In Platonis Alcibiadem
, 191, 14–18), and in the
twelfth century by Tzetzes (
Chiliades
, II, 132–133). In
Plutarch we find only a paraphrasing of the concept
expressed, while the citation becomes apparently literal in
Pappus. In the Byzantine period is added a touch of real-
ism, with the phrase given in the dialect of Syracuse, as
though it had just been heard. All of the authors mentioned
connect the words of Archimedes to the invention of a
machine for hoisting weights. However, their opinions
differ on exactly what type of machine it was: according
to Plutarch it was a
polyspaston
, for Pappus and Olym-
piodorus it was a
baroulcus
, while for Simplicius it was
a
charistion
. Tzetzes does not mention any direct
2
For a long time the passage of Galen was interpreted as the first
testimony of the use of the mirrors to set Roman ships on fire. That
interpretation, however, was based on the attribution of the meaning
of ‘burning mirror’ to the Greek term
ptqei
9
om
, which might also refer
to incendiary substances.
3
The best translation into a Western language is found in Rashed [
8
].
Lett Mat Int (2013) 1:91–95
93
123
relationship to the statement, but just before he had men-
tioned a
trispaston
. All of the authors, except for Tzetzes,
the most recent, clarify the logical nexus between the
statement and the Archimedean theory of mechanics,
which makes it possible to design machines with a high
degree of mechanical advantage (that is, a favourable ratio
between weight lifted and force acting). The logical rela-
tionship is particularly clear in the passages of Pappus and
Simplicius. For example, Pappus writes:
In this way we learn how to move a given weight
with a given force. It is said that this section of
Mechanics is one of Archimedes’ discoveries and that
when he discovered it he said, ‘‘Give me a place to
stand on, and I will move the world for you!’’ Heron
of Alexandria gave a most clear exposition of this
operation
…
In his book ‘‘Barulcus’’, however, he
explains how a given weight is moved by a given
power
…
[Pappus 1970
5
, Book 8, sect. 19].
Plutarch alone collocates the famous phrase in relation
with the likewise famous experimental demonstration in
which Archimedes pushed a ship into the sea by himself,
thanks to a machine that he had designed. The episode of
the ship is, however, also told by Proclus (
In primum Eu-
clidis Elementorum librum commentarii
, 63 [Proclus 1873
7
]), who relates it to the launch of the ship
Syracusia
.
Athenaeus (
Deipnosophistae
, V, 207b), our essential
source about this ship, speaks of the launch omitting fan-
ciful details such as that of the machine operated by a
single man, but underlining Archimedes’ essential contri-
bution. The most recent author, Tzetzes, recounts the epi-
sode of the ship without placing it in relation with the
Syracusia
(
Chiliades
, II, 110–111), but adding of his own
initiative that Archimedes could have pushed it into the sea
with only his left hand.
The episode of Archimedes in which he intuits the way
to expose the fraud relative to the crown of Hiero II while
bathing is so famous that it doesn’t need to be told in detail.
The image of Archimedes who, elated by his discovery,
jumps out of the bath and runs nude through the city cry-
ing, ‘
Eureka! Eureka!
’ is perhaps the most popular of all
those told about the great Syracusan scientist. The story is
told succinctly in Plutarch (
Non posse suaviter vivi
secundum Epicurum
, 1094 B–C) and Proclus (
In primum
Euclidis Elementorum librum commentarii
, 63 [Proclus
1873
7
]) but the version that has taken root in the collective
imagination is the longer version transmitted by Vitruvius
(
De Architectura
, IX, Introduction, 9–12). Several points
should be underlined. First of all there is an abyss between
Vitruvius’s account and the depth of Archimedean hydro-
statics as it appears in his treatise
On Floating Bodies
.In
the second place, it should be noted that not even on the
episode of the crown, which is certainly marginal, is the
account of Vitruvius the most reliable. A much more
serious description of the procedure used by Archimedes to
unmask the goldsmith, if for no other reason than it actu-
ally uses Archimedean hydrostatics, is contained in an
anonymous work that is much less well known, dating to
about 400
A
.
D
.(
Carmen de ponderibus et mensuris
,
125–155). As is always the case, here too the better-known
account is not the most reliable, but is the one that is so
superficial that it requires no effort on the part of the
reader.
Archimedes has often been presented as a scientist who
was uninterested in the concrete world and so lost in
abstract considerations and theories that he completely lost
touch with reality. This image, which has resulted in an
archetype adapted to later scientists as well, was trans-
mitted above all by Plutarch, who relates more than once
that the servants had to drag forcefully Archimedes to
bathe, while he continued to draw geometric figures where
he could, on his own stomach if nothing else was available
(
Vita Marcelli
, 17, 11–12;
Non posse suaviter vivi secun-
dum Epicurum
, 1094 B;
An seni respublica gerenda sit
,
786C). Plutarch also insists on his lack of interest in the
applications of his own theories, since he would have
considered this only a vulgar by-product of pure science,
the only thing that genuinely interested him (
Vita Marcelli
,
14, 3–4; 17, 3–4). It is amazing that for a long time
Archimedes’ attitude towards the applications of science
were deduced from the acritical acceptance of the opinion
of Plutarch: a polygraph who lived centuries later, in a
cultural climate that was completely different, certainly
could not have known the intimate thoughts of the scientist.
On the other hand, the dedication with which Archimedes
developed applications of all kinds is well documented: of
catoptrica
, as Apuleius tells in the passage already cited
(
Apologia
, 16), of hydrostatics (from the design of clocks
4
to naval engineering: we know from Athenaeus (
Deipno-
sophistae
, V, 206d) that the largest ship in Antiquity, the
Syracusia
, was constructed under his supervision), and of
mechanics (from machines to hoist weights to those for
raising water and devices of war).
In the final analysis, the testimonies regarding Archi-
medes should be taken with a grain of salt, and are cer-
tainly more useful for extracting factual information that
for deriving psychological information. The little that we
really know about Archimedes’ personality we can deduce
from his works and from the facts documented. What
emerges is a personality extraordinary for its total control
of all aspects of a unified science, one which had not yet
been divided up into mathematics, physics and technology:
4
A treatise on the construction of water-clocks, conserved in three
Arabic manuscripts, has been published in an English translation by
Hill [
2
].
94
Lett Mat Int (2013) 1:91–95
123
from the choice of the postulates to technological appli-
cations. We can, however, discern some human traits of the
scientist: from the profound intellectual honesty shown in
the treatise
The Method
, in which he decides to explain not
only his results but also the procedures that he followed to
discover them, a subtle sense of humour and probably an
ironic attitude towards the scientists of Alexandria, which
emerges more than once. The ‘cattle problem’, which we
know in the form of an epigram, is practically unsolvable
(the minimum solution is given by numbers with 206,545
digits) but it is proposed as a proof to judge the level of
mathematical proficiency: the irony is suggested above all
by the correspondent whom Archimedes wished to put to
the test: the great Eratosthenes, the leader of the Alexan-
drian scientists.
5
In another case, Archimedes is responsi-
ble for a genuine hoax. Tired of hearing it said that the
results he had announced had also been obtained inde-
pendently by other scientists, Archimedes communicated
to his Alexandrian correspondents that he had solved a
series of problems: only some time later (when, presum-
ably, his rivals had claimed credit for the same results as
independently theirs), he revealed that the ‘solutions’ that
he had announced were completely wrong (
De lineis spi-
ralibus
, 8–10 [Mugler 1970–1972
4
]).
6
It would be very
interesting to know the identity of the victims of the hoax
and what their reactions were.